The stream power river incision model: evidence, theory and beyond

2013 ◽  
Vol 39 (1) ◽  
pp. 38-61 ◽  
Author(s):  
Dimitri Lague
Keyword(s):  
Evidence Theory ◽  
Stream Power ◽  
River Incision ◽  
Model Evidence

scholarly journals Landscape evolution models using the stream power incision model show unrealistic behavior when <i>m</i> ∕ <i>n</i> equals 0.5

2017 ◽  
Vol 5 (4) ◽  
pp. 807-820 ◽  
Author(s):  
Jeffrey S. Kwang ◽  
Gary Parker
Keyword(s):  
Steady State ◽  
Landscape Evolution ◽  
Drainage Area ◽  
Uplift Rate ◽  
Stream Power ◽  
River Incision ◽  
Vertical Incision ◽  
Small Scales ◽  
Insight Into

Abstract. Landscape evolution models often utilize the stream power incision model to simulate river incision: E = KAmSn, where E is the vertical incision rate, K is the erodibility constant, A is the upstream drainage area, S is the channel gradient, and m and n are exponents. This simple but useful law has been employed with an imposed rock uplift rate to gain insight into steady-state landscapes. The most common choice of exponents satisfies m ∕ n = 0.5. Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only on small scales) is neglected, the choice m ∕ n = 0.5 yields a curiously unrealistic result: the predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 10 km2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 1000 km2 domain.

scholarly journals River profile response to normal fault growth and linkage: An example from the Hellenic forearc of south-central Crete, Greece

2016 ◽  
Author(s):  
Sean F. Gallen ◽  
Karl W. Wegmann
Keyword(s):  
Drainage Basin ◽  
Profile Analysis ◽  
Normal Fault ◽  
Drainage Area ◽  
Fault System ◽  
Stream Power ◽  
River Incision ◽  
South Central ◽  
History Of ◽  
Fault Growth

Abstract. Topography is a reflection of the tectonic and geodynamic processes that act to uplift the Earth's surface and the erosional processes that work to return it to base level. Numerous studies have shown that topography is a sensitive recorder or tectonic signals. A quasi-physical understanding of the relationship between river incision and rock uplift has made the analysis of fluvial topography a popular technique for deciphering relative, and some argue absolute, histories of rock uplift. Here we present results from a study of the fluvial topography from south-central Crete demonstrating that river longitudinal profiles indeed record the relative history of uplift, but several other processes make it difficult to recover quantitative uplift histories. Prior research demonstrates that the south-central coastline of Crete is bound by a large (~100 km long) E-W striking composite normal fault system. Marine terraces reveal that it is uplifting between 0.1–1.0 mm yr−1. These studies suggest that two normal fault systems, the offshore Ptolemy and onshore South-Central Crete faults linked together in the recent geologic past (Ca. 0.4–1 Myrs bp). Fault mechanics predicts that when adjacent faults link into a single fault the uplift rate in the linkage zone will increase rapidly. Using river profile analysis we show that rivers in south-central Crete record the relative uplift history of fault growth and linkage, as theory predicts that they should. Calibration of the commonly used stream power incision model shows that the slope exponent, n, is ~ 0.5, contrary to most studies that find n ≥ 1. Analysis of fluvial knickpoints shows that migration distances are not proportional to upstream contributing drainage area, as predicted by the stream power incision model. Maps of the transformed stream distance variable, χ, indicate that drainage basin instability, drainage divide migration and river capture events complicate river profile analysis in south-central Crete. Waterfalls are observed in southern Crete and appear to operate under less efficient and different incision mechanics than assumed by the stream power incision model. Drainage area exchange and waterfall formation are argued to obscure linkages between empirically derived metrics and quasi-physical descriptions of river incision, making is difficult to quantitatively interpret rock uplift histories from river profiles in this setting. Karst hydrology, break down of assumed drainage area-discharge scaling and chemical weathering might also contribute to the failure of the stream power incision model to adequately predict the behavior of the fluvial system in south-central Crete.

scholarly journals Parameterization of river incision models requires accounting for environmental heterogeneity: insights from the tropical Andes

2020 ◽  
Vol 8 (2) ◽  
pp. 447-470 ◽  
Author(s):  
Benjamin Campforts ◽  
Veerle Vanacker ◽  
Frédéric Herman ◽  
Matthias Vanmaercke ◽  
Wolfgang Schwanghart ◽  
...  
Keyword(s):  
Spatial Patterns ◽  
Rainfall Variability ◽  
Nonlinear Relationship ◽  
Stream Power ◽  
Denudation Rates ◽  
River Incision ◽  
Power Models ◽  
Bedrock River Incision ◽  
Lithological Heterogeneity

Abstract. Landscape evolution models can be used to assess the impact of rainfall variability on bedrock river incision over millennial timescales. However, isolating the role of rainfall variability remains difficult in natural environments, in part because environmental controls on river incision such as lithological heterogeneity are poorly constrained. In this study, we explore spatial differences in the rate of bedrock river incision in the Ecuadorian Andes using three different stream power models. A pronounced rainfall gradient due to orographic precipitation and high lithological heterogeneity enable us to explore the relative roles of these controls. First, we use an area-based stream power model to scrutinize the role of lithological heterogeneity in river incision rates. We show that lithological heterogeneity is key to predicting the spatial patterns of incision rates. Accounting for lithological heterogeneity reveals a nonlinear relationship between river steepness, a proxy for river incision, and denudation rates derived from cosmogenic radionuclide (CRNs). Second, we explore this nonlinearity using runoff-based and stochastic-threshold stream power models, combined with a hydrological dataset, to calculate spatial and temporal runoff variability. Statistical modeling suggests that the nonlinear relationship between river steepness and denudation rates can be attributed to a spatial runoff gradient and incision thresholds. Our findings have two main implications for the overall interpretation of CRN-derived denudation rates and the use of river incision models: (i) applying sophisticated stream power models to explain denudation rates at the landscape scale is only relevant when accounting for the confounding role of environmental factors such as lithology, and (ii) spatial patterns in runoff due to orographic precipitation in combination with incision thresholds explain part of the nonlinearity between river steepness and CRN-derived denudation rates. Our methodology can be used as a framework to study the coupling between river incision, lithological heterogeneity and climate at regional to continental scales.

scholarly journals Quantifying the competing influences of lithology and throw rate on bedrock river incision

2020 ◽  
Author(s):  
E. Kent ◽  
A.C. Whittaker ◽  
S.J. Boulton ◽  
M.C. Alçiçek
Keyword(s):  
Rock Type ◽  
Active Faults ◽  
Sedimentary Rocks ◽  
Normal Fault ◽  
Metamorphic Rocks ◽  
Stream Power ◽  
Western Turkey ◽  
River Incision ◽  
Bedrock River Incision

River incision in upland areas is controlled by prevailing climatic and tectonic regimes, which are increasingly well described, and the nature of the bedrock lithology, which is still poorly constrained. Here, we calculated downstream variations in stream power and bedrock strength for six rivers crossing a normal fault in western Turkey, to derive new constraints on bedrock erodibility as function of rock type. These rivers were selected because they exhibit knick zones representing a transient response to an increase in throw rate, driven by fault linkage. Field measures of rock mass strength showed that the metamorphic units (gneisses and schists) in the catchments are ∼2 times harder than the sedimentary lithologies. Stream power increases downstream in all rivers, reaching a maxima upstream of the fault within the metamorphic bedrock but declining markedly where softer sedimentary rocks are encountered. We demonstrate a positive correlation between throw rate and stream power in the metamorphic rocks, characteristic of rivers obeying a detachment-limited model of erosion. We estimated bedrock erodibility in the metamorphic rocks as kb = 2.2−6.3 × 10−14 ms2 kg−1; in contrast, bedrock erodibility values were 5−30 times larger in the sedimentary units, with kb = 1.2−15 × 10−13 ms2 kg−1. However, in the sedimentary units, stream power does not scale predictably with fault throw rate, and we evaluated the extent to which the friable nature of the outcropping clastic bedrock alters the long-term erosional dynamics of the rivers. This study places new constraints on bedrock erodibilities upstream of active faults and demonstrates that the strength and characteristics of underlying bedrock exert a fundamental influence on river behavior.

scholarly journals River profile response to normal fault growth and linkage: an example from the Hellenic forearc of south-central Crete, Greece

2017 ◽  
Vol 5 (1) ◽  
pp. 161-186 ◽  
Author(s):  
Sean F. Gallen ◽  
Karl W. Wegmann
Keyword(s):  
Profile Analysis ◽  
Normal Fault ◽  
Drainage Area ◽  
Uplift Rate ◽  
Stream Power ◽  
River Incision ◽  
South Central ◽  
History Of ◽  
River Profiles ◽  
Fault Growth

Abstract. Topography is a reflection of the tectonic and geodynamic processes that act to uplift the Earth's surface and the erosional processes that work to return it to base level. Numerous studies have shown that topography is a sensitive recorder of tectonic signals. A quasi-physical understanding of the relationship between river incision and rock uplift has made the analysis of fluvial topography a popular technique for deciphering relative, and some argue absolute, histories of rock uplift. Here we present results from a study of the fluvial topography from south-central Crete, demonstrating that river longitudinal profiles indeed record the relative history of uplift, but several other processes make it difficult to recover quantitative uplift histories. Prior research demonstrates that the south-central coastline of Crete is bound by a large ( ∼  100 km long) E–W striking composite normal fault system. Marine terraces reveal that it is uplifting between 0.1 and 1.0 mm yr−1. These studies suggest that two normal fault systems, the offshore Ptolemy and onshore South-Central Crete faults, linked together in the recent geologic past (ca. 0.4–1 My BP). Fault mechanics predict that when adjacent faults link into a single fault the uplift rate in footwalls of the linkage zone will increase rapidly. We use this natural experiment to assess the response of river profiles to a temporal jump in uplift rate and to assess the applicability of the stream power incision model to this setting. Using river profile analysis we show that rivers in south-central Crete record the relative uplift history of fault growth and linkage as theory predicts that they should. Calibration of the commonly used stream power incision model shows that the slope exponent, n, is  ∼  0.5, contrary to most studies that find n  ≥  1. Analysis of fluvial knickpoints shows that migration distances are not proportional to upstream contributing drainage area, as predicted by the stream power incision model. Maps of the transformed stream distance variable, χ, indicate that drainage basin instability, drainage divide migration, and river capture events complicate river profile analysis in south-central Crete. Waterfalls are observed in southern Crete and appear to operate under less efficient and different incision mechanics than assumed by the stream power incision model. Drainage area exchange and waterfall formation are argued to obscure linkages between empirically derived metrics and quasi-physical descriptions of river incision, making it difficult to quantitatively interpret rock uplift histories from river profiles in this setting. Karst hydrology, break down of assumed drainage area discharge scaling, and chemical weathering might also contribute to the failure of the stream power incision model to adequately predict the behavior of the fluvial system in south-central Crete.

scholarly journals Geologic constraints on bedrock river incision using the stream power law

1999 ◽  
Vol 104 (B3) ◽  
pp. 4983-4993 ◽  
Author(s):  
Jonathan D. Stock ◽  
David R. Montgomery
Keyword(s):  
Power Law ◽  
Stream Power ◽  
River Incision ◽  
Bedrock River Incision

scholarly journals Landscape evolution models using the stream power incision model show unrealistic behavior when <i>m/n</i> equals 0.5

2017 ◽  
Author(s):  
Jeffrey S. Kwang ◽  
Gary Parker
Keyword(s):  
Steady State ◽  
Landscape Evolution ◽  
Drainage Area ◽  
Uplift Rate ◽  
Stream Power ◽  
Channel Network ◽  
River Incision ◽  
Vertical Incision ◽  
Small Scales ◽  
Insight Into

Abstract. Landscape evolution models often utilize the stream power incision model to simulate river incision: E = KAmSn, where E = vertical incision rate, K = erodibility constant, A =  upstream drainage area, S = channel gradient, and m and n are exponents. This simple but useful law has been employed with an imposed rock uplift rate to gain insight into steady-state landscapes. The most common choice of exponents satisfies m/n = 0.5; indeed, this ratio has been deemed to yield the “optimal channel network.” Yet all models have limitations. Here, we show that when hillslope diffusion (which operates only at small scales) is neglected, the choice m/n = 0.5 yields a curiously unrealistic result: the predicted landscape is invariant to horizontal stretching. That is, the steady-state landscape for a 1 m2 horizontal domain can be stretched so that it is identical to the corresponding landscape for a 100 km2 domain.

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